This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
Imaging techniques based on wave equations, such as Reverse-Time Migration (RTM), have been widely applied to image the subsurface for hydrocarbon exploration. RTM is a very high fidelity imaging method which is commonly applied in complex geology settings. It is also an expensive algorithm. Furthermore, the traditional RTM image suffers from low-wavenumber noise created by backscattering energy from high-contrast boundaries in the models used by the imaging algorithm (Yoon et al., 2004; Fletcher et al., 2006; Sun et al., 2009; Douma et al., 2010). Various techniques have been tried to reduce and/or filter out the low-wavenumber noise with some level of success. These techniques range from modifications to the RTM imaging condition (Yoon et al., 2004; Douma et al., 2010), modification to the wave propagation equation to reduce the reflection from contrast boundaries in the imaging model (Fletcher et al., 2006), to the application of traditional Laplacian filter to RTM raw images (Sun and Zhang, 2009).
Different techniques have different computational intensity requirements and different effectiveness in removing the low-wavenumber noise. Techniques involving the application of different imaging conditions (Yoon et al., 2004; Douma et al., 2010) other than the direct zero-lag convolution of source and receiver wave fields or the generation of image angle gathers tend to increase the computational cost substantially.
Techniques in this category usually involve the calculation of wave propagation direction, which is an expensive operation. Also, the calculation of wave propagation direction in a complex geological area tends to have large error in the calculated wave propagation direction. This might cause leakage of the low-wavenumber noise in the image.
In practical applications, the traditional Laplacian filter technique (Sun and Zhang, 2009) is quite effective and computationally efficient. This is a post-imaging filter technique. There is no need to modify the imaging kernel, and thus the traditional efficient image condition of direct cross correlation of source and receiver wave field can be used. The filter is traditionally applied to the raw stacked image to filter out the low-wavenumber noise. Thus, it is computationally efficient. However, the traditional Laplacian filter operator is image dip independent, or isotropic. The low-wavenumber noise and other coherent noises from migration do show some directional characteristics. Despite its high efficiency, it still cannot provide a satisfactory clean image under many situations.